Bring 2 cups water to boil in a large skillet or wok. Add chopped kale and broccoli and cook for about 5 minutes, stirring occasionally, until kale and broccoli are tender. Remove kale and broccoli with slotted spoon to drain. Rinse and dry skillet, then use it to heat oil over medium-low heat. Add garlic and sautee for about 1 minute. Stir in scallions and cook for another minute.
Add cooked kale and broccoli and salt to taste. Stir to combine. Cover and cook for 1 to 2 minutes until hot. Sprinkle with sesame seeds and serve.